Universality Under Conditions of Self-tuning

We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same finite-size scaling is observed as in systems where all relevant parameters are fixed at their critical values. This scheme is studied using a self-tuning variant of the Ising model. It is contrasted with a scheme where systems approach criticality through a target value for the order parameter that vanishes with increasing system size. In the former scheme, the universal exponents are observed in naïve finite-size scaling studies, whereas in the latter they are not.     

Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide TiO _y . The effect of the long-range order of the Ti₅O₅ type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds.     

Pseudocritical NMR frequency shift above the normal-incommensurate phase transition

The NMR satellite frequencies were measured as a function of temperature in the normal high-temperature phase for ⁸⁷Rb in Rb₂ZnBr₄ and Rb₂ZnCl₄ and for ³⁵Cl in betaine calciumchloride dihydrate. Approaching the respective normal-incommensurate phase transition an anomalous shift of the NMR frequency is observed for the first two cases. This effect is ascribed to the increasing order parameter fluctuations. The experimental data are compared to calculations which relate the observed behaviour of the NMR frequencies to the non-classical critical behaviour of the substances under investigation. Received 6 August 1998     

液晶近晶C相的统计理论

采用格胞模型,由自由能极小导出了分布函数满足的积分方程。定义了分子取向序参量、质心位置序参量及两者耦合的序参量。选用适当的两体势,求得分布函数近似解和相应自由能表达式。由此知S_C—S_A相变可以是二级相变,也可以是一级相变。对TBBA,TB8A和NOBA的倾斜角和序参量随温度变化,以及相变点附近熵变和热容量,作了数值计算。还计算了TBEA和4-n-alkoxybenzylidene-4′-aminozobenzens同系物的相变温度随分子链长度的变化。结果与实验相符。 关键词：     

Temperature dependence of the Raman bandwidths and intensities of a lattice mode near the tricritical and second order phase transitions in NH4Cl

We calculate here the temperature dependence of the damping constant using the expressions derived from the Matsushita's theory and the temperature dependence of the order parameter from the molecular field theory for the tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. Our calculations are performed for the ν ₅ (174?cm^?1) Raman mode of NH₄Cl for the pressures studied. Predictions for the damping constant are in good agreement with our observed Raman bandwidths of this lattice mode for both pressures. The Raman intensities calculated from the molecular field theory by means of the order parameter are also in good agreement with our observed Raman intensities of the ν ₅ (174?cm^?1) mode for both tricritical (1.5?kbar) and second order (2.8?kbar) phase transitions in NH₄Cl. In this study our observed Raman intensities of this lattice mode are analysed using a power-law formula with the critical exponent β for the order parameter at those two pressures considered in NH₄Cl. From our analysis, the value of β?=?0.5 is obtained as the mean field value.     

Thermodynamic modeling of critical properties of ferroelectric superlattices in nano-scale

Modeling nano-scale ferroelectric superlattices using the Landau free-energy functional approach requires incorporating contributions from the interfacial and depolarization field effects. The choice of the order parameter then becomes a vital issue. In this paper, we compare the predictions of models using the spontaneous polarization as order parameter (SPOP approach) with models using the total polarization as order parameter (TPOP approach). We have comprehensively calculated the critical properties of nano-scale ferroelectric superlattices, such as the phase-transition temperature, critical thickness and Curie–Weiss-type relation using both approaches. We found that all the SPOP results are in excellent agreement with experimental measurements and first-principle calculations in all cases studied here. The TPOP approach, on the other hand, much overestimates the depolarization by underestimating the effect of the dielectric screening and produces results that deviate significantly from the experimental ones. Our results also traced the dependence of the critical properties on the thicknesses of the constituent layers of the ferroelectric superlattices to the interfacial and depolarization field effects.     

Predicting DNA–intercalator binding: the development of an arene–arene stacking parameter from SAPT analysis of benzene‐substituted benzene complexes

A series of substituted naphthalimides were synthesized and intercalated into the DNA sequence d(GCGCGCGC)₂, and an experimental ΔT_m value was obtained. Two‐parameter QSAR analyses were performed to generate a theoretical ΔT_m value. Although by no means exhaustive in terms of parameter selection, the correlations did not yield statistics that indicated the models met the threshold for significance at the 95% confidence level. Rather than continue with an exhaustive search of all possible QSAR parameters, a one‐parameter QSAR analysis was performed utilizing a novel arene–arene stacking parameter, designated Π^π, developed from Symmetry‐Adapted Perturbation Theory (SAPT) energy decomposition studies of calculated benzene‐substituted benzene dimer binding energies. The QSAR analysis using the Π^π stacking parameter yielded statistics suggesting the model was significant at the 95% confidence level. The approach of developing a novel QSAR parameter via SAPT calculations, rather than exhaustively searching all traditional QSAR parameters, is presented both as a new approach for QSAR studies and as a unique application of SAPT. Copyright © 2013 John Wiley & Sons, Ltd.     

Elastic studies of phase transitions

We report some results on acoustic studies of phase transitions in which the order parameter is coupled to the elastic wave strain, when direct behaviour observation is not possible. First by Brillouin scattering it was possible to observe the softening of C₅₅ of ammonium oxalate hemihydrate and it was concluded that the order parameter is not the deformation. In the case of members of A₂MX₄ family a softening of C₆₆ related to a shear wave near the lock-in transition was observed for [N(CH₃)₄]₂ZnCl₄, as previously found for C ₅₅ of K₂SeO₄. Such a behaviour did not occur for (NH₄)₂BeF₄ in which a strong hysteresis effect appeared.     

Magnetic transition from the paramagnetic to long-period structure in RMn2O5 multiferroics: Renormalization group analysis of critical behavior

A transition from the paramagnetic state to a long-period magnetic structure with an incommensurate wave vector along one crystallographic axis in RMn₂O₅ multiferroics is considered. An effective Hamiltonian for these oxides is constructed with allowance for spin fluctuations. Critical points are found, and their stability is analyzed using the renormalization group approach. It is shown that critical fluctuations in these compounds admit a second-order phase transition with respect to a multicomponent order parameter.     

Holographic superconductor models in the non-minimal derivative coupling theory

We study a general class of holographic superconductor models via the Stu¨ckelberg mechanism in the non-minimal derivative coupling theory in which the charged scalar field is kinetically coupling to Einstein’s tensor. We explore the effects of the coupling parameter on the critical temperature, the order of phase transitions and the critical expo- nents near the second-order phase transition point. Moreover, we compute the electrical conductivity using the probe approximation and check the ratios ω g /T c for the different coupling parameters.     

Critical behavior of RMn2O5 oxides near the magnetic phase transition to a structure incommensurate in two spatial directions

A phase transition from the paramagnetic state to the long-period magnetic structure in RMn₂O₅ oxides with the star of the wave vector determining the incommensurability of long-range magnetic order in two spatial directions has been investigated. An effective Hamiltonian of the system that allows one to describe this transition in the framework of the renormalization group approach has been constructed. It has been shown that there is a stable critical point of transformations of this group at which there occurs a second-order phase transition. The critical indices have been found. The obtained results have been compared with the results for phase transitions occurring in these oxides in accordance with the star of the wave vector, which provides incommensurability in one of the spatial directions. It has been found that fluctuations of the four-component order parameter due to the low spatial symmetry of these compounds do not change the order of the phase transition, which was found in terms of the Landau theory.     

Birefringence,X-ray and neutron diffraction measurements on the structural phase transitions of (CH3NH3)2 MnCl4 and (CH3NH3)2FeCl4

We used optical birefringence, X-ray and neutron diffraction methods with single crystals to study the structural phase transitions of the perowskite-type layer structures of (CH₃NH₃)₂MeCl₄ with Me=Mn, Fe. The Mn-compound shows the following structural transitions at 394 K — a continuous order-disorder phase transition from tetragonal symmetry $\text{I4}\text{mmm}$ to orthorhombic space group Abma (Cmca in reference 10); at 257 K — a discontinuous transition to a second tetragonal modification; at 95 K — a discontinuous transition to a monoclinic phase. For the Fe-compound the corresponding transition temperatures are 328 K and 231 K, respectively. A low temperature monoclinic phase could not be observed. The lattice parameters of the different modifications were determined as a function of temperature. The temperature dependent course of the order parameter has been investigated for the order—disorder transition. For both compounds, all the methods used gave the same value for the critical exponent of β = 0.315.     

Granular segregation as a critical phenomenon

We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated domains is defined and the effect of the variation of the combined filling fraction, C, of the mixture on the observed pattern formation is systematically studied. We find that there is a critical event associated with the onset of segregation, at C(c)=0.647+/-0.049, which has the characteristics of a continuous phase transition, including critical slowing down.     

Dynamic magnetic properties of Ising graphene-like monolayer

Dynamic magnetic properties of the mixed-spin (3/2, 5/2) Ising graphene-like monolayer in an oscillating magnetic field are studied by means of Monte Carlo simulation. The effects of Hamiltonian parameters such as crystal field and time-dependent oscillating magnetic field on the dynamic order parameter, susceptibility and internal energy of the system are well presented and explained. Moreover, much attention has also been dedicated to the phase diagrams with different parameters in order to better comprehend the impacts of these parameters on the critical temperature. Our results reveal that the crystal fields of two sublattices have similar effects on the critical temperature, but the bias field and amplitude of oscillating field have opposite effects on it. We hope that our research can be of guiding significance to the theoretical and experimental studies of graphene-like monolayer.     

Lifshitz-point behaviour of ferromagnetic superconductors

The critical behaviour of the electromagnetically coupled superconductor magnet system is investigated by means of a generalized mean field theory and a renormalization group analysis. We show that in the presence of a genuine anisotropy in systems with an additional pressure-like parameter (like concentration in pseudo-ternary ferromagnetic superconductors (FMS), e.g. Er_1?x Ho _x Rh₄B₄) the indirect coupling between superconducting and magnetic order parameters (i.e. gauge coupling) can lead to a peculiar kind of critical behaviour characterized by Lifshitz points (LP). These points (quite generally) occur as merging points of three phases: a (magnetically) disordered phase, a homogeneously ordered phase and a modulated phase. In FMS the latter phase may result from exchange screening by supercurrents. This unusual critical behaviour is found in two varieties:

1. a regular LP which may occur on the lower transition line of a reentrant FMS
2. a similar but slightly different critical point which we term modified Lifshitz point (MLP), and which is to be expected at the merging point of the upper and lower superconducting transition lines with the magnetic order disorder transition lines in the (x, T) phase diagrams of FMS's.

     

Disorder-induced quantum-Griffiths-like features from a non-conventional renormalization group analysis near four dimensions

We investigate the role played by symmetry conserving quenched disorder on quantum criticality of a variety of d-dimensional systems with a continuous symmetry order parameter. We employ a non-standard procedure which combines a preliminary reduction to an effective classical random problem and a successive conventional renormalization group treatment. Solving the effective flow equations to first order in ε=4−d and then restoring the original coupling parameters, for d<4 we find a quantum critical point scenario exhibiting unusual features, which remind us of some predictions of the quantum Griffiths phase model.     

Phase transition to anticlinic texture in free-standing smectic c films

Experimental data on the optical reflectance of free-standing smectic C films were analyzed within the framework of a phenomenological Landau approach. At a certain temperature T _0N (determined from experimental data), which exceeds the known temperature T _c of the volume phase transition from smectic A to smectic C state, a surface phase transition takes place whereby molecules in the surface layer become sloped relative to the normal of the smectic layers. The transition temperatures T _0N ^s,a for N-layer films possessing synclinic (symmetric) and anticlinic (antisymmetric) textures of the order parameter (tilt angle θ) were determined. A comparison of the theoretical and experimental data allowed all parameters of the model to be determined (including critical indices of the correlation length and the surface order parameter). Three possible models of the transition from the state with transverse polarization (perpendicular to the molecular tilt plane) to the state with longitudinal polarization (parallel to this plane) are analyzed. The transition takes place at low (°–°) values of the order parameter θ in the middle layer of the film.     

Optical and dielectric properties of the mesogen 4-cyano-4′-n–octyl biphenyl as a function of temperature

The effect of temperature on certain optical and dielectric properties of one member, namely 4-cyano-4′-n–octyl biphenyl (8CB) of the mesogenic series 4-cyano-4′-n–alkyl biphenyl (nCB), is reported. The dependence of the ordinary and extraordinary components of polarisability, α_o and α_e, on temperature is studied using a He–Ne laser beam, and the variation of orientational order parameter with temperature in the entire mesogenic phase determined from the optical studies. The dependence of the effective molecular dipole moment, μ_eff, in the liquid-crystal phase, and the angle of inclination, β, of the dipole moment with the preferred direction have been investigated. An experimental estimate of the correlation factor ‘g’, which is indicative of the nature of the molecular association in the mesophase, has been obtained.     

Molecular orientation of lyotropic nematic phase in a mixture of two non-mesogenic compounds

We report the results of our studies on the optical and thermal properties of the mixture of two non-mesogenic compounds, namely, sodium dodecyl sulfate (SDS) and glacial acetic acid (GAA). The mixture exhibits very interesting schlieren texture of lyotropic micellar nematic (N_D) phase, SmA and SmB phases, respectively, at different concentrations of SDS in GAA sequentially when the specimen is cooled from its isotropic phase. The order parameter (S) of the lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The experimental curve showing the temperature variation of order parameter is very well fitted with the Mayer–Saupe theoretical curve. X-ray studies have also been discussed. The formation of the above phases has been confirmed by optical and differential scanning calorimetry studies.